Multistage stochastic programming (MSP) is a framework for sequential decision making under uncertainty where the decision space is typically high dimensional and involves complicated constraints, and the uncertainty is modeled by a general stochastic process. In the traditional risk neutral setting, the goal is to find a sequence of decisions or a policy so as to optimize an expected value objective. MSP has found applications in a variety of important sectors including energy, finance, manufacturing, services, and natural resources. Due to the combined challenges of uncertainty, dynamics, and optimization, the resulting problems in this framework are extremely difficult. Motivated by its technical challenges and application potential there has been a great deal of research on MSP. Major progress has been made on theoretical issues such as structure, complexity and approximability, as well as on effective decomposition algorithms. This lecture will survey some of this progress.